It is unclear whether or not anyone sins in Billy Budd. Sin is an unambiguous word. It means that an action is fundamentally wrong. In the novel, however, everyone's actions seem to be in part motivated by good and in part motivated by evil, in part in their control and in part not. Yet, as a reader, there is an enormous desire to declare some characters evil and others good. Whether or not any single action can be called a sin, the idea of sin pervades the pages of Billy Budd and the fear of sin is a huge motivating factor for many of the characters.
Claggart's sin is not accusing Billy Budd; it is refusing to admit to his envy and attempting to master it.
As the narrator presents it, the only character capable of sinning in the novel is Captain Vere, because he is the only character presented as being in control of his actions.